新高考數(shù)學(xué)二輪復(fù)習(xí)講義專題04 函數(shù)及其性質(zhì)（原卷版）

專題04講：函數(shù)及其性質(zhì)【考點專題】1．函數(shù)函數(shù)兩個集合A，B設(shè)A，B是兩個非空數(shù)集對應(yīng)關(guān)系f：A→B如果按照某種確定的對應(yīng)關(guān)系f，使對于集合A中的任意一個數(shù)x，在集合B中都有唯一確定的數(shù)f(x)和它對應(yīng)名稱稱f：A→B為從集合A到集合B的一個函數(shù)函數(shù)記法函數(shù)y＝f(x)，x∈A2.函數(shù)的三要素(1)定義域：x的取值范圍；(2)值域：y的取值范圍.(3)對應(yīng)關(guān)系f：A→B.3．相等函數(shù)：定義域、對應(yīng)關(guān)系都一致.4．函數(shù)的表示法：解析法、圖象法和列表法．5．分段函數(shù)若函數(shù)在其定義域的不同子集上，因?qū)?yīng)關(guān)系不同而分別用幾個不同的式子來表示，這種函數(shù)稱為分段函數(shù)．6．函數(shù)的單調(diào)性(1)單調(diào)函數(shù)的定義增函數(shù)減函數(shù)定義一般地，設(shè)函數(shù)f(x)的定義域為I，區(qū)間D?I，如果?x1，x2∈D當(dāng)x1<x2時，都有f(x1)<f(x2)，那么就稱函數(shù)f(x)在區(qū)間D上單調(diào)遞增，特別地，當(dāng)函數(shù)f(x)在它的定義域上單調(diào)遞增時，我們就稱它是增函數(shù)當(dāng)x1<x2時，都有f(x1)>f(x2)，那么就稱函數(shù)f(x)在區(qū)間D上單調(diào)遞減，特別地，當(dāng)函數(shù)f(x)在它的定義域上單調(diào)遞減時，我們就稱它是減函數(shù)圖象描述自左向右看圖象是上升的自左向右看圖象是下降的(2)單調(diào)區(qū)間的定義如果函數(shù)y＝f(x)在區(qū)間D上單調(diào)遞增或單調(diào)遞減，那么就說函數(shù)y＝f(x)在這一區(qū)間具有(嚴格的)單調(diào)性，區(qū)間D叫做y＝f(x)的單調(diào)區(qū)間．7．函數(shù)的最值前提設(shè)函數(shù)y＝f(x)的定義域為I，如果存在實數(shù)M滿足條件(1)?x∈I，都有f(x)≤M；(2)?x0∈I，使得f(x0)＝M(1)對于?x∈I，都有f(x)≥M；(2)?x0∈I，使得f(x0)＝M結(jié)論M為最大值M為最小值8．函數(shù)的奇偶性奇偶性定義圖象特點偶函數(shù)一般地，設(shè)函數(shù)f(x)的定義域為I，如果?x∈I，都有－x∈I，且f(－x)＝f(x)，那么函數(shù)f(x)就叫做偶函數(shù)關(guān)于y軸對稱奇函數(shù)一般地，設(shè)函數(shù)f(x)的定義域為I，如果?x∈I，都有－x∈I，且f(－x)＝－f(x)，那么函數(shù)f(x)就叫做奇函數(shù)關(guān)于原點對稱9．周期性(1)周期函數(shù)：對于函數(shù)y＝f(x)，如果存在一個非零常數(shù)T，使得當(dāng)x取定義域內(nèi)的任何值時，都有f(x＋T)＝f(x)，那么就稱函數(shù)y＝f(x)為周期函數(shù)，稱T為這個函數(shù)的周期．(2)最小正周期：如果在周期函數(shù)f(x)的所有周期中存在一個最小的正數(shù)，那么這個最小正數(shù)就叫做f(x)的最小正周期．(3)函數(shù)周期性常用結(jié)論對f(x)定義域內(nèi)任一自變量的值x：(1)若f(x＋a)＝－f(x)，則T＝2a(a>0)．(2)若f(x＋a)＝eq\f(1,fx)，則T＝2a(a>0)．(3)若f(x＋a)＝－eq\f(1,fx)，則T＝2a(a>0)．(4)若f(x＋a)＋f(x)＝c，則T＝2a(a>0，c為常數(shù))．10．對稱性對稱性的三個常用結(jié)論(1)若函數(shù)f(x)滿足f(a＋x)＝f(b－x)，則y＝f(x)的圖象關(guān)于直線x＝eq\f(a＋b,2)對稱．(2)若函數(shù)f(x)滿足f(a＋x)＝－f(b－x)，則y＝f(x)的圖象關(guān)于點eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(a＋b,2)，0))對稱．(3)若函數(shù)f(x)滿足f(a＋x)＋f(b－x)＝c，則函數(shù)f(x)的圖象關(guān)于點eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(a＋b,2)，\f(c,2)))對稱．【方法技巧】1．求函數(shù)值域的一般方法：①分離常數(shù)法；②配方法；③不等式法；=4\*GB3④單調(diào)性法；=5\*GB3⑤換元法；=6\*GB3⑥數(shù)形結(jié)合法；=7\*GB3⑦導(dǎo)數(shù)法．2．確定函數(shù)單調(diào)性的四種方法(1)定義法：利用定義判斷．(2)導(dǎo)數(shù)法：適用于初等函數(shù)、復(fù)合函數(shù)等可以求導(dǎo)的函數(shù)．(3)圖象法：由圖象確定函數(shù)的單調(diào)區(qū)間需注意兩點：一是單調(diào)區(qū)間必須是函數(shù)定義域的子集；二是圖象不連續(xù)的單調(diào)區(qū)間要分開寫，用“和”或“，”連接，不能用“∪”連接．(4)性質(zhì)法：利用函數(shù)單調(diào)性的性質(zhì)，尤其是利用復(fù)合函數(shù)“同增異減”的原則時，需先確定簡單函數(shù)的單調(diào)性．3．函數(shù)單調(diào)性應(yīng)用問題的常見類型及解題策略(1)比較大?。?2)求最值．(3)解不等式．利用函數(shù)的單調(diào)性將“f”符號去掉，轉(zhuǎn)化為具體的不等式求解，應(yīng)注意函數(shù)的定義域．(4)利用單調(diào)性求參數(shù)．①依據(jù)函數(shù)的圖象或單調(diào)性定義，確定函數(shù)的單調(diào)區(qū)間，與已知單調(diào)區(qū)間比較．②需注意若函數(shù)在區(qū)間[a，b]上單調(diào)，則該函數(shù)在此區(qū)間的任意子區(qū)間上也單調(diào)．③分段函數(shù)的單調(diào)性，除注意各段的單調(diào)性外，還要注意銜接點的取值．4．利用函數(shù)奇偶性可以解決以下問題(1)求函數(shù)值：將待求值利用奇偶性轉(zhuǎn)化為求已知解析式的區(qū)間上的函數(shù)值．(2)求解析式：將待求區(qū)間上的自變量轉(zhuǎn)化到已知解析式的區(qū)間上，再利用奇偶性的定義求出．(3)求解析式中的參數(shù)：利用待定系數(shù)法求解，根據(jù)f(x)±f(－x)＝0得到關(guān)于參數(shù)的恒等式，由系數(shù)的對等性得方程(組)，進而得出參數(shù)的值．(4)畫函數(shù)圖象：利用函數(shù)的奇偶性可畫出函數(shù)在其對稱區(qū)間上的圖象．(5)求特殊值：利用奇函數(shù)的最大值與最小值之和為零可求一些特殊結(jié)構(gòu)的函數(shù)值．【核心題型】題型一：求函數(shù)的定義域1．（2012·山東·高考真題（文））函數(shù)SKIPIF1<0的定義域為（）A．[－2，0)∪(0，2] B．(－1，0)∪(0，2]C．[－2，2] D．(－1，2]2．（2021·全國·高一專題練習(xí)）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，則SKIPIF1<0的定義域為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2011·河北衡水·三模（理））已知函數(shù)的定義域為R，則實數(shù)k的取值范圍是（）A． B． C． D．題型二：求函數(shù)的值域4．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若存在SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國·高三專題練習(xí)）高斯是德國著名的數(shù)學(xué)家，近代數(shù)學(xué)奠基者之一，享有“數(shù)學(xué)王子”的稱號，用其名字命名的“高斯函數(shù)”為：設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過SKIPIF1<0的最大整數(shù)，則SKIPIF1<0稱為高斯函數(shù).例如：SKIPIF1<0，SKIPIF1<0，已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的值域為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·全國·高一課時練習(xí)）已知函數(shù)SKIPIF1<0的值域是SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是___________.題型三：復(fù)合函數(shù)的單調(diào)性7．（2022·全國·高三專題練習(xí)）下列四個函數(shù)中既是奇函數(shù)，又是增函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2020·寧夏·青銅峽市寧朔中學(xué)高三階段練習(xí)（理））設(shè)函數(shù)SKIPIF1<0，則使得SKIPIF1<0成立的x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2019·福建省長樂第一中學(xué)高一階段練習(xí)）函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0題型四：根據(jù)函數(shù)的單調(diào)性與奇偶性解不等式10．（2020·全國·高一課時練習(xí)）已知函數(shù)SKIPIF1<0是定義在R上的偶函數(shù),且在區(qū)間SKIPIF1<0單調(diào)遞增.若實數(shù)a滿足SKIPIF1<0,則a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022·全國·高三專題練習(xí)）設(shè)SKIPIF1<0為定義在R上的奇函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0(SKIPIF1<0為常數(shù))，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·湖南師大附中高三階段練習(xí)）已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，且對任意的SKIPIF1<0，都有SKIPIF1<0SKIPIF1<0，則滿足不等式SKIPIF1<0的SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型五：奇偶函數(shù)對稱性的應(yīng)用13．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0，則SKIPIF1<0的零點的個數(shù)為（

）A．6 B．7 C．8 D．914．（2022·全國·高一課時練習(xí)）設(shè)SKIPIF1<0為定義在R上的函數(shù)，函數(shù)SKIPIF1<0是奇函數(shù).對于下列四個結(jié)論：①SKIPIF1<0；②SKIPIF1<0；③函數(shù)SKIPIF1<0的圖象關(guān)于原點對稱；④函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱；其中，正確結(jié)論的個數(shù)為（

）A．1 B．2 C．3 D．415．（2022·江蘇·揚州中學(xué)高三開學(xué)考試）已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)且滿足SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）.若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型六：函數(shù)周期性的應(yīng)用16．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0的零點個數(shù)是（

）A．2 B．3 C．4 D．517．（2019·全國·高三專題練習(xí)（文））定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足：對任意的實數(shù)SKIPIF1<0都有SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0．則SKIPIF1<0的值為（）A．2017 B．1010 C．1008 D．218．（2009·山東·高考真題（理））已知定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且在區(qū)間SKIPIF1<0上是增函數(shù),若方程SKIPIF1<0在區(qū)間SKIPIF1<0上有四個不同的根，則SKIPIF1<0題型七：由函數(shù)對稱性求函數(shù)值或參數(shù)19．（2022·全國·高一課時練習(xí)）已知函數(shù)SKIPIF1<0，滿足SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2022·全國·高一課時練習(xí)）設(shè)定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0，滿足對任意的SKIPIF1<0都有SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的值等于（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的圖象關(guān)于原點對稱，且滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題型八：不等式恒（能）成立問題22．（2021·浙江·模擬預(yù)測）已知函數(shù)SKIPIF1<0，則SKIPIF1<0是SKIPIF1<0恒成立的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分不必要條件23．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若對于任意的實數(shù)x，不等式SKIPIF1<0恒成立，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2022·廣西·桂電中學(xué)高三階段練習(xí)）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0，SKIPIF1<0．若對SKIPIF1<0，SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<025．（2023·全國·高三專題練習(xí)）若SKIPIF1<0，使SKIPIF1<0成立，則實數(shù)SKIPIF1<0的取值范圍是______________．26．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則SKIPIF1<0的值域是___________.設(shè)函數(shù)SKIPIF1<0，若對于任意實數(shù)SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立，則實數(shù)SKIPIF1<0的取值范圍是___________27．（2020·全國·高二課時練習(xí)（文））已知SKIPIF1<0，SKIPIF1<0，若對SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是_________.【高考必刷】一、選擇題1．（2007·江西·高考真題（文））函數(shù)SKIPIF1<0的定義域為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2013·山東·高考真題（文））函數(shù)SKIPIF1<0的定義域是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2020·浙江溫州·高一競賽）已知集合SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高一單元測試）已知函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的定義域為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2007·湖北·高考真題（理））設(shè)SKIPIF1<0，則SKIPIF1<0的定義域為（）．A．（－4,0)∪（0,4)B．（－4，－1)∪（1,4)C．（－2，－1)∪（1,2)D．（－4，－2)∪（2,4)6．（2023·全國·高三專題練習(xí)）高斯是德國著名的數(shù)學(xué)家，近代數(shù)學(xué)奠基者之一，享有“數(shù)學(xué)王子”的美譽，用其名字命名的“高斯函數(shù)”：設(shè)SKIPIF1<0，用SKIPIF1<0表示不超過SKIPIF1<0的最大整數(shù)，則SKIPIF1<0稱為高斯函數(shù)，也稱取整函數(shù)，例如：SKIPIF1<0，SKIPIF1<0.已知SKIPIF1<0，則函數(shù)SKIPIF1<0的值域為（

）A．SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，0，SKIPIF1<07．（2008·重慶·高考真題（理））已知函數(shù)SKIPIF1<0＋SKIPIF1<0的最大值為M，最小值為m，則SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2022·新疆·烏市八中高二期末（文））設(shè)SKIPIF1<0，SKIPIF1<0，若對于任意SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2018·全國·高三課時練習(xí)（文））已知函數(shù)SKIPIF1<0，則下列說法錯誤的是（

）A．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增 B．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減C．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱 D．SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱11．（2021·全國·高一專題練習(xí)）設(shè)SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0在SKIPIF1<0上是減函數(shù)，又SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2019·河南·淇濱高中高一期中）已知函數(shù)SKIPIF1<0，且SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2021·全國·高一課時練習(xí)）在SKIPIF1<0上定義的函數(shù)SKIPIF1<0是偶函數(shù)，且SKIPIF1<0，若SKIPIF1<0在區(qū)間SKIPIF1<0上是減函數(shù)，則SKIPIF1<0（）A．在區(qū)間SKIPIF1<0上是增函數(shù)，在區(qū)間SKIPIF1<0上是增函數(shù)B．在區(qū)間SKIPIF1<0上是增函數(shù)，在區(qū)間SKIPIF1<0上是減函數(shù)C．在區(qū)間SKIPIF1<0上是減函數(shù)，在區(qū)間SKIPIF1<0上是增函數(shù)D．在區(qū)間SKIPIF1<0上是減函數(shù)，在區(qū)間SKIPIF1<0上是減函數(shù)14．（2021·全國·高一課時練習(xí)）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足：當(dāng)SKIPIF1<0時，SKIPIF1<0，則在SKIPIF1<0上方程SKIPIF1<0的實根個數(shù)為（

）A．1 B．3 C．2 D．202115．（2021·廣西·一模（理））已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，且SKIPIF1<0是偶函數(shù)，SKIPIF1<0是奇函數(shù)，SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<016．（2018·全國·高考真題（文））已知SKIPIF1<0是定義域為SKIPIF1<0的奇函數(shù),滿足SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<017．（2021·貴州·安順市第三高級中學(xué)高三階段練習(xí)（文））若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0且SKIPIF1<0時，SKIPIF1<0，則方程SKIPIF1<0的根的個數(shù)是()A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<018．（2018·新疆烏魯木齊·一模（文））奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0(

)A．-2 B．SKIPIF1<0 C．SKIPIF1<0 D．219．（2022·四川·成都金蘋果錦城第一中學(xué)高三期中（文））已知定義域是R的函數(shù)SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．-1 C．2 D．-320．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0滿足SKIPIF1<0對任意SKIPIF1<0恒成立，又函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱，且SKIPIF1<0則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．（2020·全國·高考真題（文））已知函數(shù)f(x)=sinx+SKIPIF1<0，則（）A．f(x)的最小值為2 B．f(x)的圖象關(guān)于y軸對稱C．f(x)的圖象關(guān)于直線SKIPIF1<0對稱 D．f(x)的圖象關(guān)于直線SKIPIF1<0對稱22．（2022·全國·高一課時練習(xí)）對SKIPIF1<0，不等式SKIPIF1<0恒成立，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<023．（2023·全國·高三專題練習(xí)）不等式SKIPIF1<0恒成立，則實數(shù)k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．（2018·新疆烏魯木齊·一模（文））已知SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．（2022·全國·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0，其中SKIPIF1<0，若存在唯一整數(shù)SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．（2021·全國·高一課時練習(xí)）當(dāng)SKIPIF1<0時，若關(guān)于SKIPIF1<0的不等式SKIPIF1<0有解，則實數(shù)SKIPIF1<0的取值范圍是（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<027．（2022·全國·高三專題練習(xí)）若存在正數(shù)SKIPIF1<0使SKIPIF1<0成立，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題28．（2022·全國·高三專題練習(xí)）定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0且SKIPIF1<0在SKIPIF1<0上是增函數(shù)，給出下列真命題的有（

）A．SKIPIF1<0是周期函數(shù)；B．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱；C．SKIPIF1<0在SKIPIF1<0上是減函數(shù)；D．SKIPIF1<0.29．（2022·全國·高一課時練習(xí)）若定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，在區(qū)間SKIPIF1<0上，有SKIPIF1<0，則下列說法正確的是（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0成中心對稱B．函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0成軸對稱C．在區(qū)間SKIPIF1<0上，SKIPIF1<0為減函數(shù)D．SKIPIF1<030．（2022·江蘇·高郵市第一中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0是定義在R上的奇函數(shù)，SKIPIF1<0是偶函數(shù)，當(dāng)SKIPIF1<0，則下列說法中正確的有（

）A．函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對稱B．4是函數(shù)SKIPIF1<0的周期C．SKIPIF1<0D．方程SKIPIF1<0恰有4不同的根31．（2022·全國·高三專題練習(xí)）已知三次函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象關(guān)于點（1，0）對稱，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0有3個零點C．SKIPIF1<0的對稱中心是SKIPIF1<0 D．SKIPIF1<0三、填空題32．（2007·重慶·高考真題（理））若函數(shù)f(x)＝SKIPIF1<0的定義域為R，則a的取值范圍為________．33．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是____________．34．（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，則函數(shù)SKIPIF1<0的值域為________．35．（2022·廣東·模擬預(yù)測）設(shè)定義域